Yeah, there are a ton of them actually. If you check PDSH wiki, and look at the category "Humor" you will find Hoppy, the Marvel Bunny, Wiggles the Worm, and Lockjaw, the crocodile, for starters. If you check the Free Universe site (link in my signature), you will find a page called, "Paw World" which lists half a dozen PD funny animal characters (but mostly of the superhero variety). If you look up, "Public Domain Funnies wiki" you will find about 25 more humor and romance characters. But there are many, many more besides....you just have to skim through all the humor comics on Digital Comic Museum. Just make sure, they aren't reprints of copyrighted newspaper strips.
Probably the most famous cute/funny animals in the public domain are Peter Rabbit and Felix the Cat. I don't think Peter is PD in its native England until 2014, but he should be here in the United States. The same author came up with dozens of other animal characters, that share the same status. Another character named Peter Rabbit, aka Peter Cottontail, originating in the United States, is also PD. Only the original version of Felix is PD.
Other good PD sources for cute or funny animals: Wind in the Willows, Alice in Wonderland, Through the Looking Glass and the first dozen Wizard of Oz novels.
Subject: Funny Animals 
